MATLAB-based Implementation of Finite-Element-Method 基于Matlab的有限元方法实现

This matlab code is capable of simulating mechanical structures, which can be discretized into one of these 3 Finite Elements: Plane Frame Element, Constant Strain Triangular Element or Eight Nodes Quadrilateral Element.

Author: Marco Yangjun Liu, [email protected]

Read the FEA Simulation Manual for more details

1 The Plane Frame Element

Step 1 Discretizing the rigid frame (Inputting data)

Step 2 Calculating the element stiffness matrix

Step 3 Assembling element stiffness matrixes and get the frame stiffness matrix

Step 4 Constraint handling: applying the boundary conditions

Step 5 Solving the system of linear equations (in global coordinate system)

Step 6 Calculating nodal internal forces of each beam (in local coordinate system)

2 The Constant Strain Triangular Element

Step 1 Discretizing the structure (Inputting data)

Step 2 Calculating the element stiffness matrix

Step 3 Assembling element stiffness matrixes

Step 4 Applying the boundary conditions and calculating the unknown displacements and reactions

Step 5 Calculating the element stress vectors

3 The Eight Nodes Quadrilateral Element

Step 1 Discretizing the structure (Inputting data)

Step 2 Calculating the element stiffness matrix

Step 3 Assembling element stiffness matrices

Step 4 Applying the boundary conditions and calculating the unknown displacements and reactions

Step 5 Calculating the element stress vectors

Simulation Results

Citation

If you are using this MATLAB FEM code, please add the following citation to your publication:

@misc{liu2021mif,
  author = {Yangjun Liu},
  title = {MATLAB-based Implementation of Finite-Element-Method},
  year = {2021},
  publisher = {GitHub},
  journal = {GitHub Repository},
  howpublished = {\url{https://github.com/RealMarco/Finite-Element-Method}}
}